Reviews In Ring Theory
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| Author | : Donald S. Passman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 324 |
| Release | : 2004-09-28 |
| Genre | : Mathematics |
| ISBN | : 9780821869383 |
Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index
| Author | : Lance W. Small |
| Publisher | : |
| Total Pages | : 608 |
| Release | : 1981 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Paul M. Cohn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 234 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1447104757 |
A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
| Author | : T.Y. Lam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475739877 |
Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.
| Author | : Nathan Jacobson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 160 |
| Release | : 1943-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821815024 |
The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
| Author | : Hideyuki Matsumura |
| Publisher | : Cambridge University Press |
| Total Pages | : 338 |
| Release | : 1989-05-25 |
| Genre | : Mathematics |
| ISBN | : 9780521367646 |
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 387 |
| Release | : 1980-07-24 |
| Genre | : Mathematics |
| ISBN | : 0080874002 |
Polynomial Identities in Ring Theory
| Author | : S.K. Jain |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 330 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461219787 |
| Author | : Lance W. Small |
| Publisher | : |
| Total Pages | : 712 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Huishi Li |
| Publisher | : World Scientific |
| Total Pages | : 295 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814365149 |
1. Preliminaries. 1.1. Presenting algebras by relations. 1.2. S-graded algebras and modules. 1.3. [symbol]-filtered algebras and modules -- 2. The [symbol]-leading homogeneous algebra A[symbol]. 2.1. Recognizing A via G[symbol](A): part 1. 2.2. Recognizing A via G[symbol](A): part 2. 2.3. The [symbol-graded isomorphism A[symbol](A). 2.4. Recognizing A via A[symbol] -- 3. Grobner bases: conception and construction. 3.1. Monomial ordering and admissible system. 3.2. Division algorithm and Grobner basis. 3.3. Grobner bases and normal elements. 3.4. Grobner bases w.r.t. skew multiplicative K-bases. 3.5. Grobner bases in K[symbol] and KQ. 3.6. (De)homogenized Grobner bases. 3.7. dh-closed homogeneous Grobner bases -- 4. Grobner basis theory meets PBW theory. 4.1. [symbol]-standard basis [symbol]-PBW isomorphism. 4.2. Realizing [symbol]-PBW isomorphism by Grobner basis. 4.3. Classical PBW K-bases vs Grobner bases. 4.4. Solvable polynomial algebras revisited -- 5. Using A[symbol] in terms of Grobner bases. 5.1. The working strategy. 5.2. Ufnarovski graph. 5.3. Determination of Gelfand-Kirillov Dimension. 5.4. Recognizing Noetherianity. 5.5. Recognizing (semi- )primeness and PI-property. 5.6. Anick's resolution over monomial algebras. 5.7. Recognizing finiteness of global dimension. 5.8. Determination of Hilbert series -- 6. Recognizing (non- )homogeneous p-Koszulity via A[symbol]. 6.1. (Non- )homogeneous p-Koszul algebras. 6.2. Anick's resolution and homogeneous p-Koszulity. 6.3. Working in terms of Grobner bases -- 7. A study of Rees algebra by Grobner bases. 7.1. Defining [symbol] by [symbol]. 7.2. Defining [symbol] by [symbol]. 7.3. Recognizing structural properties of [symbol] via [symbol]. 7.4. An application to regular central extensions. 7.5. Algebras defined by dh-closed homogeneous Grobner bases -- 8. Looking for more Grobner bases. 8.1. Lifting (finite) Grobner bases from O[symbol]. 8.2. Lifting (finite) Grobner bases from a class of algebras. 8.3. New examples of Grobner basis theory. 8.4. Skew 2-nomial algebras. 8.5. Almost skew 2-nomial algebras
